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dejp-tem4

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Patterns in Nature



Broad Question: What is a fractal in nature?

Specific Question: Can we see symmetry of a seashell by measuring its fractals?

Variables

Independent Variable: whorls of the seashell

Dependent Variable: length of the whorls in comparison to one another

Variables That Need To Be Controlled: type of shell & the type of measurement being used

Hypothesis: I predict that we will see symmetry (of a seashell) by measuring its fractals because fractals are geometric patterns that show the pattern of something no matter how close-up.

Graph of Hypothesis:

deja's_hypothesis_graph.jpg

General Plan:

Experimental Design: I am going to conduct an experiment to determine if symmetry can be found in a seashell by measuring its fractals. The experiment will be conducted at my school, A Crosby Kennett Middle School, and at my home. I am going to bring the materials to my home if and when I go there. I am the only person that will be involved in the experiment. I will measure, from suture to suture, the whorls of the seashell and see if there is a diminishing pattern from the larger end of the shell to the smaller end.

The type of seashell that I'll use will be an Auger shell. I will be measuring/testing five Auger shells to get the best results. I will make a data/observation table to record the results of my measurements; by hand and then onto the computer when I finish. I have a camera on my phone, which I will use to take pictures of the experiment throughout the experiment. After the pictures are taken I'll upload them onto the Wiki page.

Materials List:

1.) Auger shells (5)

2.) caliber

3.) Piece of paper to record data

4.) a ruler with centimeters

5.) surface to work on (flat)

6.) a writing utensil

Background Research:

"Fractal." World Book. 12 ed. 2009. Print
Fractal,FRAK tuhl, is a complex geometric figure made up of patterns that repeat themselves at smaller and smaller scales. Any of its smallest structures is similar in shape to a larger structure, which, in turn, is similar to an even larger one, and so on. The characteristic of looking alike at different scales is known as self-similarity
"Naturally Occurring Fractals." Miqel.com. Miqel.com, 2006-2007. Web. 8 Feb. 2012.
“Many things previously called chaos are now known to follow subtle subtle fractal laws of behavior. So many things turned out to be fractal that the word "chaos" itself (in operational science) had redefined, or actually for the FIRST time Formally Defined as following inherently unpredictable yet generally deterministic rules based on nonlinear iterative equations. Fractals are unpredictable in specific details yet deterministic when viewed as a total pattern - in many ways this reflects what we observe in the small details & total pattern of life in all it's physical and mental varieties, too.
After a few dozen repetitions or ITERATIONS the shape we would recognize as a Perfect Fern appears from the abstract world of math. How and Why can this be?
The answer to why is that it Simply IS - and it's quite surprising too!
Answering How is that nature always follows the simplest & most efficient path. Fractals are maps of the simplest paths sliding up the scale of Dimensions (from 2-D to 3-D and so on). So maybe it's simply an artifact of nature's elegance that we find exact correspondences between these inherently existing mathematical forms and natural patterns, and even living creatures of many types.


Fractals in nature are ubiquitous - clouds, plants, galaxies, shells and more.”
Winder , Jessica. Parts of the shell – Common Whelk. 2010. Jessica's Nature Blog. Web. 10 Feb. 2012.
Diagram of a shell(image).
external image placeholder?w=200&h=137
"What is a Fractal?." Solar Flares. 27 Oct. 1999. Web. 10 Feb. 2012.
"Fractals are extensions of traditional Euclidean shapes, such as lines, squares, and circles, with two fundamental properties. First, when you view fractals, you can magnify them an infinite number of times, and they contain structure at every magnification level. Second, you can generate fractals using finite and typically small sets of instructions and data."

References:

Procedure:

1.) Go home (or wherever experiment will be conducted).

2.) Gather all materials.

3.) Take Auger shell A and the caliber.

4.) Measure the length of the Auger shell with the caliber.

5.) Compare the caliber to the ruler(remember to use centimeters).

6.) Record data in centimeters.

7.) Starting with the whorl at the widest end of the shell, measure from suture to suture the width of the whorl with the caliber.

8.) Compare caliber to the ruler in centimeters.

9.) Record data in centimeters.

10.) Measure the width of the next whorl with the caliber.

11.) Compare caliber to ruler.

12.) Record data in centimeters.

13.) Repeat steps 3-12 with the other Auger shells.

14.) Don't forget to take pictures throughout the entire experiment!








Results

Data Table


Graphs





Photos


Data Analysis


Conclusion

Discussion